Public Cloud computing can be seen as a "Pay as you go" model for implementing and making available information resources, applications, and even infrastructure (usually in the case of a private cloud environment). This as opposed to a "Pay for what you intend on using" model, if you want. Public clouds also most often means that you share resources with other companies/organizations.
Some of the benefits of doing this is that you don't have to fork out a gazillion bucks to get up and running, and as your organization grows, you can either move from a public-cloud type design to a hybrid-cloud design and ultimately a private cloud environment, where you run IaaS (Infrastructure as a Service) and basically own the compute infrastructure you use (Servers, Storage, Network) and these resources are used exclusively by your organization.
This is a very basic definition, but following the links above and Googling a bit you will gain a wealth of explanations and business cases.